Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

Several models within the framework of continuum mechanics have been proposed over years to solve free vibration problem micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified stress theories. Many retain basic features Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one more material scale length parameters tackle problem. The work described in this paper deals with problems beams dynamic stiffness method, through implementation theory conjunction theory. main advantage is that unlike other models, it uses only parameter account for smallness structure. current research accomplished first by solving governing differential equations motion a beam closed analytical form. matrix then formulated relating amplitudes forces corresponding displacements at ends beam. applied using Wittrick–Williams algorithm as solution technique investigate characteristics Natural frequencies mode shapes several examples presented, effects demonstrated.